We investigate effects of longitudinally varying nonlinearity on periodically distributed amplification systems in optical fibres. Emphasis is made on configurations in which the nonlinear coefficient exponentially grows or decays along the propagation distance, while the group-velocity-dispersion (GVD) coefficient is held constant. Such systems are of practical relevance to the design of highly efficient nonlinear devices, including broadband light sources and advanced amplification schemes, where precise management of the interplay between the GVD, nonlinearity, and gain is essential. Adopting the known generic integrability condition, we derive exact analytical expressions for the evolution of the optical field in the presence of the tailored nonlinearity profiles and periodically distributed gain. The resulting periodic wavetrain solutions and their long-wave limit in the form of bright and dark solitons provide insight into the controlled enhancement or suppression of nonlinear effects under realistic amplification conditions. The robustness of these solutions is examined by introducing finite perturbations and directly evaluating their effects on the corresponding intensity profiles. The structural stability of solutions against deviations from the integrability condition is demonstrated too. Outcomes of this study contribute to a deeper understanding of the nonlinear pulse dynamics in engineered gain-managed fibres and offer guidance for the development of novel optical systems, where the spatial distribution of the nonlinearity is exploited to optimise the performance.
Coherence-generating power (CGP) tells how much coherence a quantum process produces on average from incoherent inputs, but an average can hide where that coherence comes from. We introduce the coherence-generating power deviation (CGPD), the standard deviation of the generated Hilbert–Schmidt coherence over the uniform simplex of incoherent states. CGPD turns coherence generation into a landscape: a small value signals robust production across input populations, whereas a large value reveals selective conversion of particular population imbalances. By representing unitary coherence generation as a quadratic response on population space, we obtain exact first and second moments in arbitrary finite dimension. We prove that every nontrivial unitary generator must fluctuate, and we separate this unavoidable isotropic fluctuation from excess anisotropy. The resulting distinction between average strength and input selectivity has direct consequences for benchmarking, reliability guarantees, input-ensemble susceptibility, and four-copy measurement protocols; it also extends naturally to unital quantum channels. Matched quantum-walk and quasiperiodic-transport examples show that topology and localization can leave CGP unchanged while substantially changing CGPD, revealing structure invisible to the mean alone.
We theoretically investigate a 0-π transition in a WSe2-based Josephson junction under anoff-resonant right circularly polarized light. By using the Dirac-Bogoliubov-de Gennes equation, we demonstrate that the light-induced gap provides an effective approach to manipulate the Josephson current. The additional phase accumulation acquired by Cooper pairs in the illuminated WSe2 region modifies the interference of Andreev bound states, resulting in a reversal of the critical Josephson current. Furthermore, the critical Josephson current exhibits oscillatory sign reversals with increasing light-induced gap, indicating multiple light-modulated transitions between 0 and π states. The junction length also serves as an effective geometric parameter to control the 0-π transition through length-dependent phase accumulation. Our results provide a feasible route for optical manipulation of 0-π transition in WSe2 and offer potential applications in superconducting quantum devices.
